The Far North line between Ardgay and Golspie and again from Helmsdale to Thurso and Wick is way longer than by road. The legacy of landlowners with far too much power, probably the descendants of the Duke of Sutherland and likes responsible for the Highland Clearances that blighted the area.
Is it? Wikipedia says the Helmsdale-Wick section was built on that route to avoid the Berriedale Braes, and the massive amount of civil engineering you'd need to build a railway through that area. The railway follows the Strath of Kildonan instead, which is relatively flat. They did build a railway line to Lybster, but that went NW to Wick rather than SE to Helmsdale.
Dornoch also used to be served by a railway going north from there, and I can't see which way a railway could go from Ardgay. They did consider diverting the railway across the Dornoch Firth Bridge when they were planning it in the 1980s, which could have saved up to 45 minutes on the journey, but they decided against it.
For some figures on the detours the Far North Line takes (road figures from
freemaptools.com, and I don't know what assumptions they make for road travel):
Wick-Helmsdale: 30.4m air, 35.9m road, 60 rail (97% or 67% further).
Golspie-Tain: 11.1m air, 16.6m road, 40.25m rail (263% or 142% further).
Invergordon-Inverness: 14.5m air, 24.3m road, 31.5m rail (117% or 30% further).
The road also takes a circuitous route north of Inverness as they decided not to build the Cromarty Bridge too close to Cromarty.
If you're going between Barrow and Carlisle I'd say that the direct train along the coast is a sensible route as you don't need to worry about changing trains. It's quicker to change at Lancaster but is it actually more convenient?
The tickets are also much cheaper that way. I would say that is a strong argument for "normal" people using it by itself.
An indirect route with a different history is Altincham-Manchester Piccadilly. It's 7.9 miles by air, 9.4 by road and 15.25 by rail (94% or 61% further) as the direct line was repurposed for Metrolink.